zengfung’s notes
Zeng Fung Liew
2/7/2021
Import data
Univariate EDA
Predictor variables
## year
## 1982 1983 1984 1985 1986 1987 1988
## 48 48 48 48 48 48 48
Question: do we want to round down the drink age? Then make this categorical?
## drinkage
## 18 18.5 19 19.1599998474121
## 12 3 49 1
## 19.25 19.5 19.6700000762939 20
## 2 2 6 20
## 20.25 20.3299999237061 20.5 21
## 1 2 6 232
Response variables
Multivariate EDA
mean response plot:
jail and service have shown slight increase by year.
drinkage have mainly shifted from 18-19 in 1982 to 21 in 1988.
## year
## jail 1982 1983 1984 1985 1986 1987 1988
## no 39 35 34 33 33 34 33
## yes 9 13 14 15 15 14 14## year
## service 1982 1983 1984 1985 1986 1987 1988
## no 43 40 39 38 38 38 37
## yes 5 8 9 10 10 10 10## year
## drinkage_cat 1982 1983 1984 1985 1986 1987 1988
## 18 5 4 3 2 1 0 0
## 19 13 13 13 11 8 1 1
## 20 6 6 6 5 3 3 0
## 21 24 25 26 30 36 44 47
dont think unemployment rate is a good predictor, as it doesnt fit our goals from this analysis. can add into the discussion sections tho
percentage of young drivers have decreased over the years as the number of states that changed their drinkage to 21 has increased. however, later on (if i use a mixed effects model) drinkage is not exactly a good predictor (not significant).
Model fitting
Note: goal is to observe whether the type of law implemented to tacker drunk driving can actually prevent fatalities
- panel linear model, using state as panel
not entirely sure how to interpret themodel="within"part.
if i index on “state”, beertax is not a significant predictor.
if i index on “year”, drinkage is not a significant predictor
## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = afatal_prop ~ beertax + jail + service + drinkage,
## data = Fatalities, model = "within", index = "state")
##
## Unbalanced Panel: n = 48, T = 6-7, N = 335
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.3434894 -0.0256639 -0.0016049 0.0204173 0.2303012
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## beertax 0.0581056 0.0527138 1.1023 0.2712746
## jailyes 0.1431230 0.0398392 3.5925 0.0003861 ***
## serviceyes -0.1659102 0.0454909 -3.6471 0.0003156 ***
## drinkage -0.0179305 0.0048585 -3.6906 0.0002683 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 0.85673
## Residual Sum of Squares: 0.76982
## R-Squared: 0.10145
## Adj. R-Squared: -0.060485
## F-statistic: 7.98754 on 4 and 283 DF, p-value: 4.1001e-06- lmer model with state as random effect
## Linear mixed model fit by REML ['lmerMod']
## Formula: afatal_prop ~ beertax + jail + service + drinkage_cat + (1 |
## state)
##
## REML criterion at convergence: -870.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.1340 -0.5009 -0.0677 0.3450 4.3716
##
## Random effects:
## Groups Name Variance Std.Dev.
## state (Intercept) 0.003654 0.06044
## Residual 0.002775 0.05268
## Number of obs: 335, groups: state, 48
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.323416 0.023070 14.019
## beertax 0.028628 0.018412 1.555
## jailyes 0.051174 0.020429 2.505
## serviceyes -0.060080 0.023645 -2.541
## drinkage_cat19 0.004721 0.020154 0.234
## drinkage_cat20 -0.003560 0.021885 -0.163
## drinkage_cat21 -0.029759 0.019295 -1.542
##
## Correlation of Fixed Effects:
## (Intr) beertx jailys srvcys drn_19 drn_20
## beertax -0.455
## jailyes -0.165 0.105
## serviceyes 0.074 -0.140 -0.707
## drinkg_ct19 -0.714 0.021 -0.017 0.006
## drinkg_ct20 -0.684 0.053 0.006 -0.021 0.741
## drinkg_ct21 -0.798 0.065 0.018 -0.052 0.852 0.809## Analysis of Variance Table
## npar Sum Sq Mean Sq F value
## beertax 1 0.005926 0.0059257 2.1353
## jail 1 0.002295 0.0022946 0.8268
## service 1 0.024149 0.0241490 8.7021
## drinkage_cat 3 0.036160 0.0120535 4.3435if i use year as random effect, it seems that drink age does not really correlate to alcohol fatalities.
if i use state as random effect, jail is not a significant predictor of alcohol fatalities
- regular lm model
state and year are highly significant predictors, but they are not what we’re after
if we dont include them this causes drinkage and jail to not be significant predictors
##
## Call:
## lm(formula = afatal_prop ~ beertax + jail + service + drinkage_cat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.15167 -0.04933 -0.01266 0.03183 0.31359
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.333335 0.021241 15.693 < 2e-16 ***
## beertax 0.021209 0.009058 2.341 0.01981 *
## jailyes 0.029612 0.011361 2.606 0.00957 **
## serviceyes -0.033531 0.013259 -2.529 0.01191 *
## drinkage_cat19 -0.016357 0.022627 -0.723 0.47026
## drinkage_cat20 -0.013554 0.024907 -0.544 0.58668
## drinkage_cat21 -0.030126 0.020851 -1.445 0.14947
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07785 on 328 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.0539, Adjusted R-squared: 0.03659
## F-statistic: 3.114 on 6 and 328 DF, p-value: 0.005561## Analysis of Variance Table
##
## Response: afatal_prop
## Df Sum Sq Mean Sq F value Pr(>F)
## beertax 1 0.02485 0.024846 4.0999 0.043697 *
## jail 1 0.01760 0.017596 2.9035 0.089333 .
## service 1 0.04768 0.047679 7.8676 0.005333 **
## drinkage_cat 3 0.02312 0.007708 1.2719 0.283966
## Residuals 328 1.98771 0.006060
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Trying out with transformation of variables
seems like it’s slightly better, but its way harder to interpret the findings now 
- panel linear model
## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = inv_afatal_prop ~ beertax + jail + service + drinkage,
## data = Fatalities, model = "within", index = "state")
##
## Unbalanced Panel: n = 48, T = 6-7, N = 335
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -1.7839032 -0.2311134 -0.0084016 0.2317763 3.3822809
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## beertax -0.560960 0.473780 -1.1840 0.2374022
## jailyes -0.769675 0.358065 -2.1495 0.0324394 *
## serviceyes 1.061066 0.408862 2.5952 0.0099473 **
## drinkage 0.167551 0.043667 3.8370 0.0001536 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 68.028
## Residual Sum of Squares: 62.186
## R-Squared: 0.085881
## Adj. R-Squared: -0.078854
## F-statistic: 6.64693 on 4 and 283 DF, p-value: 3.9891e-05- random effects model
jail is still the least significant
## Linear mixed model fit by REML ['lmerMod']
## Formula: inv_afatal_prop ~ beertax + jail + service + drinkage_cat + (1 |
## state)
## Data: Fatalities
##
## REML criterion at convergence: 564
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7833 -0.5384 -0.0229 0.4705 6.9891
##
## Random effects:
## Groups Name Variance Std.Dev.
## state (Intercept) 0.2923 0.5406
## Residual 0.2201 0.4691
## Number of obs: 335, groups: state, 48
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.22168 0.20577 15.657
## beertax -0.24334 0.16453 -1.479
## jailyes -0.35388 0.18244 -1.940
## serviceyes 0.50986 0.21115 2.415
## drinkage_cat19 -0.07405 0.17954 -0.412
## drinkage_cat20 0.01671 0.19496 0.086
## drinkage_cat21 0.28737 0.17190 1.672
##
## Correlation of Fixed Effects:
## (Intr) beertx jailys srvcys drn_19 drn_20
## beertax -0.455
## jailyes -0.165 0.105
## serviceyes 0.075 -0.140 -0.708
## drinkg_ct19 -0.713 0.021 -0.017 0.005
## drinkg_ct20 -0.683 0.053 0.006 -0.021 0.741
## drinkg_ct21 -0.797 0.065 0.018 -0.052 0.852 0.809## Analysis of Variance Table
## npar Sum Sq Mean Sq F value
## beertax 1 0.4591 0.45910 2.0861
## jail 1 0.0108 0.01075 0.0489
## service 1 1.8334 1.83345 8.3309
## drinkage_cat 3 3.8888 1.29628 5.8901- fixed effects model
##
## Call:
## lm(formula = inv_afatal_prop ~ beertax + jail + service + drinkage_cat,
## data = Fatalities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7803 -0.4054 -0.0128 0.4130 2.4503
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.03998 0.19093 15.922 < 2e-16 ***
## beertax -0.18028 0.08142 -2.214 0.02750 *
## jailyes -0.28295 0.10212 -2.771 0.00591 **
## serviceyes 0.33929 0.11918 2.847 0.00469 **
## drinkage_cat19 0.20729 0.20338 1.019 0.30885
## drinkage_cat20 0.18321 0.22388 0.818 0.41376
## drinkage_cat21 0.42582 0.18742 2.272 0.02373 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6997 on 328 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.07924, Adjusted R-squared: 0.06239
## F-statistic: 4.704 on 6 and 328 DF, p-value: 0.0001305## Analysis of Variance Table
##
## Response: inv_afatal_prop
## Df Sum Sq Mean Sq F value Pr(>F)
## beertax 1 1.795 1.7949 3.6658 0.056410 .
## jail 1 1.632 1.6322 3.3335 0.068789 .
## service 1 5.346 5.3457 10.9180 0.001058 **
## drinkage_cat 3 5.047 1.6824 3.4361 0.017215 *
## Residuals 328 160.597 0.4896
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1